Model Functions Little App

In this app, you select a response variable and an explanatory variable, as well as (optionally) a covariate.

The app automatically builds a model of the response variable in terms of the explanatory variable and covariate (if any). The model is displayed along with the data.

The first step is to go to the “Data” tab. There you can choose from a library of data sets, a specific data frame from that library, and response and explanatory variables. The data and a model of the response in terms of the explanatory variables will be shown immediately.

The buttons near the top of the app allow you to

• set the size n of the sample
• : draw a new sample
• : freeze the current display so that you can compare it to new samples that you take. You can update the frozen display simply by pressing the button again.
• : make model choices such as flexibility and model type
• Randomize the response variable, implementing a Null Hypothesis

At the bottom of the apps are several tabs that give different displays of the situation:

• Data: Where you pick a data frame and response and explanatory variables. There are buttons here for displaying this page of explanation and the codebook for the data frame you have chosen.
• Graph: The main display of the current sample of data.
• Compare: Side-by-side displays of the current sample and the last sample frozen by you.
• Stats: Statistics summarizing the current sample (and the last sample frozen)

Randomize response

Often, you want to compare the model you got with the actual data to a model constructed with data simulated from the null hypothesis of no relationship between the response and explanatory variables. The simulated data is identical to the actual data except the response variable values have been shuffled.

For instance, you might build a model with randomization OFF, then freeze the display. Next, turn randomization ON and compare the simulated results to the actual results you have already frozen.

Statistics

This app automatically builds a model of the response variable as a function of the explanatory variable. The statistics shown are:

• the variance of the response variable
• the variance of the model values
• the sample size, n
• R²
• the degrees of flexibility of the model
• the F statistic

Response and model values

You can tell the app to display the distribution of the response and model values. (See the Graph and Compare tabs.) The I-bar shows the mean ± 1 and 2 times the standard deviation. (The variance, shown in the statistics report, is the square of the standard deviation.)